Question

if x+ y =5 and xy =6,then find xcube +y cube​

Answer 1

(x+y)=5

xy=6

Then,

x³+y³=(x+y)(x²-xy+y²)=5×(x²+y²-xy)

=5×[(x+y)²-2xy-xy]=5×[(5)²-3×6]

=5×(25-18)=5×7=35 Ans...

Or You Can answer it as

(x+y)³=x³+y³+3xy(x+y)

=>x³+y³=(x+y)³-3xy(x+y)

=>x³+y³=(5)³-3×6×5=125-90=35Ans.

Hope You Understand it Well

Happy To Help✌️

Answer 2

Answer:

Given that :

x + y = 5

Cubing both the sides -

(x + y)³ = (5)³

⇒ x³ + y³ + 3xy (x + y) = 125

⇒ x³ + y³ + 3 * 6 * 5 = 125 [xy = 6]

⇒ x³ + y³ + 90 = 125

⇒ x³ + y³ = 125 - 90

⇒ x³ + y³ = 35

Hence, the answer is 35.

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$\large{\underline{\underline{\mathfrak{Extra \: Information -}}}}$

$\boxed{\begin{minipage}{6 cm} \underline{Algebraic Identities:} \\ \\ \sf (a + b)^2=a^2+ 2ab +b^2 \\ \\ (a - b)^2 = a^2-2ab + b^2 \\ \\ (a+b)^3 = a^3 + b^3 + 3ab (a+b) \end{minipage}}$